Solve for $x$ and $y$ using elimination. ${-4x+3y = 6}$ ${3x-4y = -22}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $4$ and the bottom equation by $3$ ${-16x+12y = 24}$ $9x-12y = -66$ Add the top and bottom equations together. $-7x = -42$ $\dfrac{-7x}{{-7}} = \dfrac{-42}{{-7}}$ ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {-4x+3y = 6}\thinspace$ to find $y$ ${-4}{(6)}{ + 3y = 6}$ $-24+3y = 6$ $-24{+24} + 3y = 6{+24}$ $3y = 30$ $\dfrac{3y}{{3}} = \dfrac{30}{{3}}$ ${y = 10}$ You can also plug ${x = 6}$ into $\thinspace {3x-4y = -22}\thinspace$ and get the same answer for $y$ : ${3}{(6)}{ - 4y = -22}$ ${y = 10}$